restoring John's version

Author: oscarbranson

book/05_globalenvironment/l34.md

@@ -1,7 +1,7 @@
 (lecture_34)=
 # Thermohaline Circulation
 
-<!-- In the previous section, we examined the shallow circulation that develops in the upper $\sim 100$m of ocean in response to wind forcing. In this section, we will examine the deep _Thermohaline Circulation_ that develops in response to wind forcing and surface heating/cooling and evaporation/precipitation.
+In the previous section, we examined the shallow circulation that develops in the upper $\sim 100$m of ocean in response to wind forcing. In this section, we will examine the deep _Thermohaline Circulation_ that develops in response to wind forcing and surface heating/cooling and evaporation/precipitation.
 
 In earlier lectures, we noted that strong poleward-flowing currents (including the Gulf Stream) develop on the western sides of the ocean basins and that these transport significant amounts of heat from low to high latitudes. Also recall from {numref}`fig:mean_ssh` the curious observation that the mean sea level is higher on the western sides of ocean basins. We will start by quantitatively explaining both of these features of the large-scale ocean circulation. A key insight that underlies the theory that we will discuss is that the Coriolis parameter, $f$ varies with latitude (recall that $f=2\Omega \sin \theta$ where $\theta$ is the latitude.
 
@@ -104,7 +104,7 @@ Hence, Eq. {eq}`eq:vorticity` is an evolution equation for the vorticity. In the
 
 Unlike the shallow wind-driven ocean circulation that we discussed in the previous lecture, the western boundary currents tend to be quite deep. For example, the Gulf Stream extends to depths below 1000m. However since the upper ocean is much warmer than the deep ocean (see {numref}`fig:WOCE_ocean_temperature`, most of the poleward heat flux occurs near the surface. To a large extent, the western boundary currents are responsible for the poleward near-surface heat flux (the upper advective flux in the Stommel model). This represents one component of the Thermohaline Circulation.
 
-As the western bondary currents flow polewards, they lose heat (see {numref}`fig:ocean_heat_flux`) and the density of the water increases. The water eventually becomes dense enough to sink to the deep ocean. This sinking occurs in relatively small areas through a process called _deep convection_. The water then spreads throughout the ocean interior and very slowly returns up to the surface. The water involved in a closed loop of the Thermohaline Circulation could travel extremely long distances, as sketched in {numref}`fig:marshall_speer` and {numref}`fig:WOCE_ocean_temperature`. It can take more than 1000 years for a parcel of water to complete this circuit. This long timescale is very important for the climate system. Since the ocean is a major reservoir of heat and carbon, the climate system has a very long `memory'. By burning fossil fuels, we are adding _antropogenic carbon_ to the ocean. Some of this carbon will remain in the ocean for more then 1000 years! -->
+As the western bondary currents flow polewards, they lose heat (see {numref}`fig:ocean_heat_flux`) and the density of the water increases. The water eventually becomes dense enough to sink to the deep ocean. This sinking occurs in relatively small areas through a process called _deep convection_. The water then spreads throughout the ocean interior and very slowly returns up to the surface. The water involved in a closed loop of the Thermohaline Circulation could travel extremely long distances, as sketched in {numref}`fig:marshall_speer` and {numref}`fig:WOCE_ocean_temperature`. It can take more than 1000 years for a parcel of water to complete this circuit. This long timescale is very important for the climate system. Since the ocean is a major reservoir of heat and carbon, the climate system has a very long `memory'. By burning fossil fuels, we are adding _antropogenic carbon_ to the ocean. Some of this carbon will remain in the ocean for more then 1000 years!
 
 ```{figure} ./figures/munk.png
 ---
@@ -115,9 +115,7 @@ width: 50%
 Temperature measurements from the eastern Pacific ocean. The vertical axis indicates depth in km. From Munk, 1966.
 ```
 
-<!-- Based on this description, we might expect the deep ocean to fill up with the very cold water that sinks at high latitudes. To some extent this is true, but the as shown in {numref}`fig:munk`, the temperature in the ocean interior is non-uniform and decreases gradually with depth. A remaining question is: if the cold water at the bottom of the ocean is gradually moving up, what is the source of heat that prevents the deep ocean from filling with the coldest water. Sunlight only penetrates the upper 10's of meters, so solar heating cannot explain the observed temperature profile.  -->
-
-Based on high latitude deep water formation, we might expect the deep ocean to fill up with the very cold water that sinks at high latitudes. To some extent this is true, but the as shown in {numref}`fig:munk`, the temperature in the ocean interior is non-uniform and decreases gradually with depth. A remaining question is: if the cold water at the bottom of the ocean is gradually moving up, what is the source of heat that prevents the deep ocean from filling with the coldest water. Sunlight only penetrates the upper 10's of meters, so solar heating cannot explain the observed temperature profile.
+Based on this description, we might expect the deep ocean to fill up with the very cold water that sinks at high latitudes. To some extent this is true, but the as shown in {numref}`fig:munk`, the temperature in the ocean interior is non-uniform and decreases gradually with depth. A remaining question is: if the cold water at the bottom of the ocean is gradually moving up, what is the source of heat that prevents the deep ocean from filling with the coldest water. Sunlight only penetrates the upper 10's of meters, so solar heating cannot explain the observed temperature profile. 
 
 A solution to this problem was proposed by Munk, 1966. Munk proposed that downward mixing of heat by small-scale turbulence balances the upward advection of cold water. To model this, he used an advection/diffusion equation for a vertical profile of temperature, $T(z,t)$ of the form